Of course! I'll solve each of the 10 problems on the worksheet for multiplying numbers in scientific notation. The key rule is:
>
To multiply two numbers in scientific notation:
> 1. Multiply the coefficients (the decimal parts).
> 2. Add the exponents of the powers of 10.
> 3. If necessary, adjust the result so it's in proper scientific notation (coefficient between 1 and 10).
Let's solve them one by one.
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Problem 1: `(9.6 × 10⁷) × (4.3 × 10⁶)`
* Multiply coefficients: `9.6 × 4.3 = 41.28`
* Add exponents: `10⁷⁺⁶ = 10¹³`
* Result: `41.28 × 10¹³`
* Adjust to proper scientific notation: Move decimal one place left → `4.128 × 10¹⁴`
✔ Answer 1: `4.128 × 10¹⁴`
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Problem 2: `(8.7 × 10⁵) × (2.4 × 10⁹)`
* Multiply coefficients: `8.7 × 2.4 = 20.88`
* Add exponents: `10⁵⁺⁹ = 10¹⁴`
* Result: `20.88 × 10¹⁴`
* Adjust: Move decimal one place left → `2.088 × 10¹⁵`
✔ Answer 2: `2.088 × 10¹⁵`
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Problem 3: `(1 × 10⁵) × (1.6 × 10⁹)`
* Multiply coefficients: `1 × 1.6 = 1.6`
* Add exponents: `10⁵⁺⁹ = 10¹⁴`
* Result: `1.6 × 10¹⁴` (Already in proper form)
✔ Answer 3: `1.6 × 10¹⁴`
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Problem 4: `(1 × 10³) × (7.7 × 10⁹)`
* Multiply coefficients: `1 × 7.7 = 7.7`
* Add exponents: `10³⁺⁹ = 10¹²`
* Result: `7.7 × 10¹²` (Already in proper form)
✔ Answer 4: `7.7 × 10¹²`
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Problem 5: `(9.04 × 10¹⁰) × (5.74 × 10⁹)`
* Multiply coefficients: `9.04 × 5.74 = 51.9096`
* Add exponents: `10¹⁰⁺⁹ = 10¹⁹`
* Result: `51.9096 × 10¹⁹`
* Adjust: Move decimal one place left → `5.19096 × 10²⁰`
✔ Answer 5: `5.19096 × 10²⁰`
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Problem 6: `(3.51 × 10⁸) × (4.9 × 10⁷)`
* Multiply coefficients: `3.51 × 4.9 = 17.199`
* Add exponents: `10⁸⁺⁷ = 10¹⁵`
* Result: `17.199 × 10¹⁵`
* Adjust: Move decimal one place left → `1.7199 × 10¹⁶`
✔ Answer 6: `1.7199 × 10¹⁶`
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Problem 7: `(9.05 × 10⁶) × (4.62 × 10³)`
* Multiply coefficients: `9.05 × 4.62 = 41.811`
* Add exponents: `10⁶⁺³ = 10⁹`
* Result: `41.811 × 10⁹`
* Adjust: Move decimal one place left → `4.1811 × 10¹⁰`
✔ Answer 7: `4.1811 × 10¹⁰`
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Problem 8: `(9.4 × 10⁹) × (2.6 × 10⁵)`
* Multiply coefficients: `9.4 × 2.6 = 24.44`
* Add exponents: `10⁹⁺⁵ = 10¹⁴`
* Result: `24.44 × 10¹⁴`
* Adjust: Move decimal one place left → `2.444 × 10¹⁵`
✔ Answer 8: `2.444 × 10¹⁵`
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Problem 9: `(5.4 × 10⁵) × (1.5 × 10³)`
* Multiply coefficients: `5.4 × 1.5 = 8.1`
* Add exponents: `10⁵⁺³ = 10⁸`
* Result: `8.1 × 10⁸` (Already in proper form)
✔ Answer 9: `8.1 × 10⁸`
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Problem 10: `(8.52 × 10⁹) × (4.47 × 10³)`
* Multiply coefficients: `8.52 × 4.47 = 38.0844`
* Add exponents: `10⁹⁺³ = 10¹²`
* Result: `38.0844 × 10¹²`
* Adjust: Move decimal one place left → `3.80844 × 10¹³`
✔ Answer 10: `3.80844 × 10¹³`
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✔ Final Answers List:
1. `4.128 × 10¹⁴`
2. `2.088 × 10¹⁵`
3. `1.6 × 10¹⁴`
4. `7.7 × 10¹²`
5. `5.19096 × 10²⁰`
6. `1.7199 × 10¹⁶`
7. `4.1811 × 10¹⁰`
8. `2.444 × 10¹⁵`
9. `8.1 × 10⁸`
10. `3.80844 × 10¹³`
Parent Tip: Review the logic above to help your child master the concept of scientific notation multiplication worksheet.
